#include <Eigen/Dense>
#include <iostream>

using namespace std;
using namespace Eigen;

int
main()
{
	Matrix3f A;
	A << 1, 2, 5, 2, 1, 4, 3, 0, 3;
	cout << "Here is the matrix A:\n" << A << endl;
	FullPivLU<Matrix3f> lu_decomp(A);
	cout << "The rank of A is " << lu_decomp.rank() << endl;
	cout << "Here is a matrix whose columns form a basis of the null-space of A:\n" << lu_decomp.kernel() << endl;
	cout << "Here is a matrix whose columns form a basis of the column-space of A:\n"
		 << lu_decomp.image(A) << endl; // yes, have to pass the original A
}
